Quick dimkid check

We were using the wrong “maximal” model! This is a quick notebook to check what we see when we use the right maximal model to determine how many factors to extract.

7-9yo US Children, 2 characters

Maximal structure, oblimin rotation

convergence not obtained in GPFoblq. 1000 iterations used. A loading greater than abs(1) was detected.  Examine the loadings carefully.

Reduced structure, oblimin rotation

Alternative factor retention methods

Parallel analysis suggests that the number of factors =  3  and the number of components =  3 

Very Simple Structure
Call: vss(x = x, n = n, rotate = rotate, diagonal = diagonal, fm = fm, 
    n.obs = n.obs, plot = plot, title = title, use = use, cor = cor)
VSS complexity 1 achieves a maximimum of 0.64  with  2  factors
VSS complexity 2 achieves a maximimum of 0.78  with  3  factors

The Velicer MAP achieves a minimum of 0.01  with  3  factors 
BIC achieves a minimum of  -2636.75  with  3  factors
Sample Size adjusted BIC achieves a minimum of  -549.78  with  5  factors

Statistics by number of factors 
  vss1 vss2    map dof chisq    prob sqresid  fit RMSEA   BIC SABIC complex
1 0.61 0.00 0.0207 740  1846 7.7e-96      48 0.61 0.091 -2093   251     1.0
2 0.64 0.77 0.0121 701  1171 3.8e-26      28 0.77 0.063 -2561  -340     1.3
3 0.57 0.78 0.0090 663   892 5.7e-09      22 0.82 0.048 -2637  -536     1.6
4 0.53 0.75 0.0096 626   803 1.9e-06      20 0.84 0.044 -2529  -545     1.9
5 0.52 0.73 0.0099 590   721 1.6e-04      18 0.85 0.041 -2419  -550     2.0
6 0.49 0.71 0.0107 555   652 2.7e-03      17 0.86 0.038 -2302  -544     2.1
7 0.50 0.71 0.0113 521   586 2.5e-02      16 0.87 0.034 -2187  -536     2.3
8 0.47 0.67 0.0121 488   527 1.1e-01      14 0.88 0.031 -2071  -525     2.4
  eChisq  SRMR eCRMS  eBIC
1   4475 0.118 0.121   536
2   1568 0.070 0.074 -2164
3    819 0.051 0.055 -2710
4    690 0.046 0.052 -2642
5    566 0.042 0.048 -2575
6    482 0.039 0.046 -2472
7    402 0.035 0.043 -2371
8    337 0.032 0.041 -2261

Clustering within reduced factor space

7-9yo US Children, 9 characters

Maximal structure, oblimin rotation

convergence not obtained in GPFoblq. 1000 iterations used. A loading greater than abs(1) was detected.  Examine the loadings carefully.

Reduced structure, oblimin rotation

Alternative factor retention methods

The estimated weights for the factor scores are probably incorrect.  Try a different factor extraction method.

Parallel analysis suggests that the number of factors =  3  and the number of components =  3 

Very Simple Structure
Call: vss(x = x, n = n, rotate = rotate, diagonal = diagonal, fm = fm, 
    n.obs = n.obs, plot = plot, title = title, use = use, cor = cor)
VSS complexity 1 achieves a maximimum of 0.82  with  1  factors
VSS complexity 2 achieves a maximimum of 0.9  with  2  factors

The Velicer MAP achieves a minimum of 0.02  with  3  factors 
BIC achieves a minimum of  -447.53  with  3  factors
Sample Size adjusted BIC achieves a minimum of  -41.12  with  7  factors

Statistics by number of factors 
  vss1 vss2   map dof chisq    prob sqresid  fit RMSEA  BIC SABIC complex
1 0.82 0.00 0.041 170   542 1.8e-40    14.1 0.82 0.141 -276   262     1.0
2 0.77 0.90 0.032 151   374 6.8e-21     8.1 0.90 0.117 -353   125     1.2
3 0.56 0.88 0.022 133   192 5.7e-04     5.2 0.93 0.068 -448   -27     1.5
4 0.57 0.88 0.027 116   156 7.9e-03     4.7 0.94 0.062 -402   -35     1.6
5 0.56 0.87 0.032 100   125 4.5e-02     4.0 0.95 0.055 -356   -40     1.7
6 0.49 0.76 0.036  85   102 1.0e-01     3.5 0.96 0.052 -307   -38     2.0
7 0.49 0.74 0.042  71    76 3.2e-01     3.0 0.96 0.039 -266   -41     2.1
8 0.48 0.77 0.048  58    55 5.8e-01     2.5 0.97 0.023 -224   -40     2.1
  eChisq  SRMR eCRMS eBIC
1    690 0.121 0.128 -128
2    279 0.077 0.087 -448
3     82 0.042 0.050 -558
4     65 0.037 0.048 -494
5     46 0.031 0.043 -435
6     32 0.026 0.039 -377
7     21 0.021 0.035 -321
8     12 0.016 0.029 -267

Clustering within reduced factor space

4-6yo US Children

Maximal structure, oblimin rotation

 A loading greater than abs(1) was detected.  Examine the loadings carefully.

Reduced structure, oblimin rotation

Alternative factor retention methods

The estimated weights for the factor scores are probably incorrect.  Try a different factor extraction method.

Parallel analysis suggests that the number of factors =  2  and the number of components =  1 

An ultra-Heywood case was detected.  Examine the results carefully

Very Simple Structure
Call: vss(x = x, n = n, rotate = rotate, diagonal = diagonal, fm = fm, 
    n.obs = n.obs, plot = plot, title = title, use = use, cor = cor)
VSS complexity 1 achieves a maximimum of 0.84  with  1  factors
VSS complexity 2 achieves a maximimum of 0.87  with  2  factors

The Velicer MAP achieves a minimum of 0.02  with  1  factors 
BIC achieves a minimum of  -521.5  with  1  factors
Sample Size adjusted BIC achieves a minimum of  -46.41  with  4  factors

Statistics by number of factors 
  vss1 vss2   map dof chisq    prob sqresid  fit RMSEA  BIC SABIC complex
1 0.84 0.00 0.018 170   298 4.7e-09    11.0 0.84 0.084 -521  16.0     1.0
2 0.62 0.87 0.019 151   242 3.5e-06     8.9 0.87 0.077 -486  -8.1     1.4
3 0.43 0.78 0.022 133   192 5.9e-04     7.8 0.88 0.068 -449 -28.2     1.9
4 0.34 0.67 0.023 116   146 3.1e-02     6.6 0.90 0.055 -413 -46.4     2.2
5 0.33 0.61 0.028 100   128 3.1e-02     5.9 0.91 0.057 -354 -37.8     2.4
6 0.32 0.60 0.033  85   104 8.1e-02     5.2 0.92 0.053 -306 -37.1     2.5
7 0.28 0.53 0.039  71    78 2.7e-01     4.5 0.93 0.042 -264 -39.8     2.6
8 0.31 0.55 0.046  58    57 5.3e-01     4.0 0.94 0.027 -223 -39.6     2.5
  eChisq  SRMR eCRMS eBIC
1    276 0.076 0.081 -544
2    180 0.062 0.069 -547
3    132 0.053 0.063 -509
4     87 0.043 0.055 -472
5     70 0.039 0.053 -412
6     53 0.033 0.050 -357
7     34 0.027 0.044 -308
8     23 0.022 0.040 -256

Clustering within reduced factor space